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We consider the quantized atom-field model and for the regime that$\hat{H}_{\cal E}\ll\hat{H}_{\cal S}\ll\hat{H'}$ (but $\hat{H}_{\cal E}\neq0$and $\hat{H}_{\cal S}\neq0$); where $\hat{H}_{\cal E}$, $\hat{H}_{\cal S}$ and$\hat{H'}$ respectively represent the self Hamiltonians of the environment andthe system, and the interaction between the system and the environment.Considering a single-mode quantized field we obtain the time-evolution operatorfor the model. Using our time-evolution operator we calculate thetime-dependent pointer states of the system and the environment (which arecharacterized by their ability not to entangle with states of anothersubsystem) by assuming an initial state of the environment in the form of aGaussian package in position space. We obtain a closed form for the offdiagonalelement of the reduced density matrix of the system and study the decoherenceof the central system in our model. We will show that for the case that thesystem initially is not prepared in one of its pointer states, the offdiagonalelement of the reduced density matrix of the system will decay with adecoherence time which is inversely proportional to the square root of the massof the bosonic field particles.

Time-dependent pointer states of the quantized atom-field model in a  nonresonance regime and consequences regarding the decoherence of the central  system